Hence, in the proposed time-varying Bradley-Terry model we do not require the strong conditions of [1]} to be met at each time point, but simply require the aggregated conditions in Theorem  to hold. This is a significant weakening of the data requirement. For example, even if one team did not play any game in a match round – a situation that would preclude the MLE in the standard Bradley-Terry model – it is still possible to assign a rank to this team in their missing round, as long a game is recorded in another round (with at least one win and one loss). In this sense, the kernel-smoothing of the data in our time-varying Bradley-Terry model reduces the required sample complexity for a unique solution.
